What is the difference between CAT and CMAT ?

A big difference. CAT is the gateway to getting admission to the IIMs. CMAT scores are not accepted by most tier 1 MBA colleges. CAT is conducted by the IIMs themselves, whereas CMAT is conducted by AICTE. Additionally, CAT is much tougher and requires much more preparation than CMAT. I can go on here, but you should get the gist of it by now.